PERCEPTUAL SEMIOSIS AND THE MICROGENESIS OF ALGEBRAIC GENERALIZATIONS1

Abstract: This paper deals with the problem of algebraic generalizations of elementary geometric-numeric patterns. It focuses on understanding the role played by the various semiotic systems mobilized by students in the progressive process of perceptual apprehension of a pattern and its generalization. The microgenetic analysis of the mathematical activity of two small groups of students in a Grade 9 class shows how making recourse to semiotic resources, such as gestures, language, and rhythm, allows the students to objectify different aspects of their spatial-temporal mathematical experience. The analysis also shows some connections between the syntax of the students ’ algebraic formulas and the semiotic means of objectification through which the formulas were forged, thereby shedding some light on the meaning of students’ algebraic expressions